Given Electric field, find the charge densities

[ybisno]

Homework Statement

Find the charge densities given the electric field (Attached question)

Relevant Equations

Electrostatics

Hi. Need help with physics homework. I was able to separate each term and find sigma from the second term and possibly lambda from the first term. Not sure how to approach the third term. (attached attempt at question)

 

[BvU]

Would you recognize the shape of the field if $z_1 = 0$ ?

(to begin with, for $|\vec r| \ge R_2$ )

 

[ybisno]

Would you recognize the shape of the field if $z_1 = 0$ ?

(to begin with, for $|\vec r| \ge R_2$ )

Yes its spherical right? could you guide me for the third term; how to find a density ?

 

[BvU]

Completely spherical around $\ (0,0,z_1)\$, yes
Any clue as to where there is no charge present ?

 

[ybisno]

No. We are currently looking to find either volume charge density or Q- charge density. That was the only hint I was given, the first two parts of my solution seem correct. Just the last term, I am struggling with.

 

[BvU]

And no clue as to where there is charge present either ?

Made a sketch of E versus r ?

 

[ybisno]

And no clue as to where there is charge present either ?

Made a sketch of E versus r ?

Not really understanding your responses...

 

[BvU]

know about Gauss's law ?

 

[ybisno]

Yes, We have just started electrostatics. I used the concept of Gauss's differential form for the first section of my answer (the second term of the Electric field with the sign(z-z0).

 

[BvU]

Hard to help without giving it away completely.
You have a spherically symmetric field, so you are looking for a spherically symmetric charge distribution. Can it be, e.g., a sphere with uniformly distributed charge of a certain size ?

 

[ybisno]

Hard to help without giving it away completely.
You have a spherically symmetric field, so you are looking for a spherically symmetric charge distribution. Can it be, e.g., a sphere with uniformly distributed charge of a certain size ?

hmm so we would need to solve for Q (Uniform charge of the sphere) but would I need to split it into two cases? r>R and r<R?

 

[BvU]

Is that really necessary ? What if R $\downarrow 0$ ?

 

[ybisno]

Is that really necessary ? What if R $\downarrow 0$ ?

I think i figured it out ! Thank you !

 

[BvU]

Point charge at (0,0,z1)